As an English speaker, but by no means an expert, the two phrases are more or less the same.
1. Her problems stem from her childhood.
2. Her problems are rooted in her childhood.
Mean more or less the same, and I wouldn't worry about any minor differences.
However, in a different sense, you can be well rooted in the ways of the world, meaning that you know the ways of the world, but you can't be well stemmed in the ways of the world!